The broad, long-term objectives of this research are to develop semiparametric regression models and associated inference procedures for the analysis of censored data, which are commonly encountered in medical studies. The Specific Aims of this renewal application include: (1) development of a structural equation modelling frame- work with semiparametric failure time models for integrative analysis of multiple genomics platforms or other complex medical data, (2) investigation of semiparametric single-index regression models to discover optimal treatment regimens for potentially censored outcomes, (3) exploration of semiparametric random-effects models with time-varying regression coefficients to predict multiple types of recurrent adverse events and to assess the lag effects of drug exposures using post-approval surveillance data, and (4) pursuit of a counting-process modeling framework for individual-level infection time data with network information to understand disease dynamics at both individual and population levels. All these Aims address important new challenges arising from the latest medical research. The estimation of the proposed models is based on likelihood and other sound statistical principles. The large-sample properties of the estimators will be established rigorously through innovative use of modern empirical process theory and other advanced mathematical tools. Efficient and stable numerical algorithms will be developed to implement the inference procedures. The proposed methods will be evaluated extensively through simulation studies mimicking real data and be applied to our ongoing medical studies, including The Cancer Genome Atlas, Cancer and Leukemia Group B clinical trials, Observational Medical Outcomes Partnership databases, and HIV/STD prevention studies in North Carolina. Efficient, reliable and user-friendly open-source software with proper documentation will be produced. The proposed work will create new paradigms in survival analysis, advance medical research at UNC and elsewhere, and accelerate the search for effective strategies to prevent and treat cancers, cardiovascular diseases, AIDS, and other diseases of utmost public health importance.